Nikolaus Conference 2023

Speaker: Maria Chlouveraki (Athens)

Title: Three Generalizations of the Temperley-Lieb algebra


The Temperley-Lieb algebra was introduced by Temperley and Lieb for its applications in statistical mechanics. It has several definitions, one of which is via a quotient of the Iwahori-Hecke algebra of type A. It is thanks to this definition that Jones was able to use the Temperley-Lieb algebra to define the famous knot invariant known as the Jones polynomial. In the past 10 years, the Yokonuma-Hecke algebra of type A, which is a generalization of the Iwahori-Hecke algebra of the same type, came into the spotlight for its topological applications. In this talk, we will study 3 possible candidates for the generalization of the Temperley-Lieb algebra in this context and declare a winner. This is joint work with Guillaume Pouchin.

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